[Copernicus]

Yes it is a zero sum game, since the sum of the payoffs to each participant is 0. Assuming there are blinds it is also finite under any strategy, since there is a non-zero probability of a player winning consecutive hands that blind out an opponent who's objective is to make the game infinite.

There is no universal optimal strategy, since it is a game of imperfect information, although I would guess that there are good game theoretical approximations to an optimal strategy based on ratios of chip counts to blinds.

It would seem that for a dominant chip leader a strategy of aggressive pre-flop play, combined with post flop betting in reasonable proportions (of the smaller stack) to his probability of beating random hands would yield something close to optimal.